Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Breaking of Galilean invariance in the hydrodynamic formulation of ferromagnetic thin films



Ezio Iacocca, Thomas J. Silva, Mark Hoefer


Microwave magnetodynamics in ferromagnets are often studied in the limit of small-amplitude modes that modulate a well-defined magnetic state. However, strongly nonlinear regimes, where the aforementioned limits are not applicable, have become experimentally accessible due to recent technological advances such as spin torque and the spin Hall effect. By re-interpreting the governing Landau- Lifshitz equation of motion, we derive an exact set of equations of dispersive hydrodynamic form that are amenable to analytical study even when full nonlinearity and exchange dispersion are included. The resulting equations are found to, in general, break Galilean invariance and a magnetic Mach number is obtained as a function of static and moving reference frames. The simplest class of solutions are termed uniform hydrodynamic states (UHS) and exhibit fluid-like behavior including laminar flow at subsonic speeds and the formation of a Mach cone and wave- fronts at supersonic speeds. A regime of modulational instability is also possible, where the UHS is violently unstable. The hydrodynamic interpretation opens up novel possibilities in magnetic research.
Physical Review Letters


magnetodynamics, Landau-Lifshitz, Galilean invariance, hydrodynamics, magnetization, spin current


Iacocca, E. , Silva, T. and Hoefer, M. (2017), Breaking of Galilean invariance in the hydrodynamic formulation of ferromagnetic thin films, Physical Review Letters, [online],, (Accessed June 16, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created January 5, 2017, Updated October 12, 2021